Some  Business  Problems 
of  AmericQLn  Forestry 


Some  Business  Problems  of 
American  Forestry 


By  C.  a.  SCHENCK,  Ph.  D., 

Forester  to  the  Biltmore  Estate,  Biltmore,  N.  C. 

Forest  Assessor  to  the  Grand  Duchy  of  Hesse- Darmstadt,  and 

Principal  Biltmore  School  of  Forestry, 


The  French  Broad  Press,  Ashcville,  N.  C. 


Digitized  by  the  Internet  Archive 

in  2009  with  funding  from 

NCSU  Libraries 


http://www.archive.org/details/somebusinessprobOOsche 


PREFACE. 

FORESTRY  on  a  large  scale  will  not  be  possible  in  the  United 
States,  on  private  holdings,  unless  it  proves  to  be  a  remun- 
erative investment  of  capital. 

Unfortunately,  ovving  to  the  slowness  of  treegrowth,  there 
is  no  chance  of  large  profits  in  forestry.  Not  one  of  the  forest  own- 
ers abroad  has  engaged  in  forestry  with  a  view  of  getting  rich 
through  it.  Forestry  is  not  a  maker  of  wealth  ;  it  is  only  a  pre- 
server of  wealth. 

As  a  preserver  of  wealth,  forestry  is  unrivalled.  No  business 
yields  interest  on  the  capital  engaged  in  it  as  steadily  as  forestry. 
As  sure  as  the  sun  shines,  the  wind  blows  and  the  rain  falls,  the 
volume  of  a  tree  is  compelled  to  increase,  the  increment  represent- 
ing the  interest  on  tree-capital.  Sunshine,  air  and  precipitations 
are  the  factors  of  treegrowth. 

Abroad,  all  aristocratic  families  owning  forest-estates  have  suc- 
ceeded in  the  maintainance  of  their  standing  for  centuries,  whilst 
the  rich  merchants  and  bankers  of  olden  times  have  not  left  a  trace 
of  their  names  and  their  wealth,  in  spite  of  the  fact,  that  many  of 
them,  the  merchants  of  Leipzig,  Hamburg,  Midland,  Nuernberg, 
were  richer  than  their  sovereigns  themselves. 

In  America,  it  is  the  well-to-do  class,  and  pre-eminently  the  well- 
to-do  lumberman,  who  should  be  interested  in  forestry,  wherever  it 
offers  him  a  safe  and  remunerative  chance  of  investment. 

The  "  Problems  of  Forestry "  were  compiled  with  a  view  of 
showing  the  American  wood  owners  the  financial  character  of  pro- 
fessional forestry.  The  object  in  forestry,  as  in  any  other  business, 
is  the  production  of  high  and  safe  interest  on  capital.  Some  little 
knowledge  of  elementary  mathematics  and  of  banking  generally 
is  required  for  the  solution  of  any  financial  problem.  The  banker, 
the  insurance  company,  the  stock  broker,  constantly  meet  with 
tasks  similar  to  those  outlined  in  the  "  Problems  of  Forestry." 

The  splendid  interest  tables  issued  by  the  Mutual  Life  Insur- 
ance Company  were  used  for  the  solution  of  the  problems  in  order 
to  avoid  the  times-taking  application  of  logarithms. 

C.A.  SCHENCK, 
Forester  to  the  Biltmore  Estate. 
Biltmore,  N.  C,  March,  1900. 


TABLE  OF  PROBLEMS. 

PAGE 

A  Longleaf  Pine  Problem  (Florida) 5 

Another  Longleaf   Pine  Problem  (Florida) 6 

A  Red  Fir  Problem  (Oregon) 8 

A  Yellow  Poplar  Problem  (North  Carolina) lO 

Another  Yellow  Poplar  Problem  (North  Carolina) la 

An  Adirondack   Problem      13 

A  Spruce  Problem 14 

Another  Spruce  Problem 16 

A  White  Pine  Problem    (Minnesota) 17 

A  Shortleaf  Pine  Problem    (Arkansas) 18 

Influence  of  Forest  Fires  on  Rate  of  Interest 20 

Stumpage — Prices  of  the  Future        21 

Forest  Taxation  in  the  United  States 22 

Influence  of  Taxes  on  Business  Forestry 23 

A  National  Park  Problem  (Minnesota) 24 

State  Loans  for  Forestry  Purposes  (Pennsylvania) 25 

Weeding  and  Road-building 26 


A  LONGLEAF  PINE  PROBLEM  (FLORIDA). 

PREMISES  :  Mr.'  S.,  of  E.,  Florida,  owns  a  pine  forest  of  all 
ages,  so  that  seedlings,  saplings,  poles  and  trees  are  equally  mixed, 
and  estimates  that  the  annual  growth  is  250  feet  board  measure  per 
acre.  The  tract  is  100,000  acres  and  he  thus  cuts  25,000,000  feet 
board  measure  annually  with  the  view  of  not  decreasing  the  growing 
stock.  The  expense  for  taxes  and  the  cost  of  protection  from  fire, 
etc.,  is  5c  per  acre  per  annum  ;  the  value  of  the  stumpage  is  $1  per 
thousand  feet  board  measure.  Mr.  S.  thinks  that  the  quality  of  the 
forest  will  be  improved  gradually,  and  expects  an  increase  in  pro- 
ductiveness, of  one  per  cent,  annually.  He  figures,  besides,  on  ris- 
ing stumpage  prices,  the  rise  keeping  step  with  the  increase  in  pop- 
ulation {i}4  per  cent.).  He  has  a  chance  to  invest  money  at  5  per 
cent,  in  an  equally  safe  manner  and  wants  to  sell  the  forest. 

QUESTION  :  Below  what  price  per  acre  is  it  not  advisable 
for  Mr.  S.  to  sell  ? 

POINTS : 

1.  Mr.  S.  must  figure  at  5  per  cent,  interest,  as  the  equally 
safe  investment  promises  him  5  per  cent,  as  well. 

2.  If  the  productiveness  of  the  forest  increases  by  i  per  cent, 
per  annum,  and  the  stumpage  price  at  i}4  per  cent,  per  annum,  the 
receipts  will  grow  at  the  rate  of  2}4  per  cent,  per  annum.  In  dis- 
counting these  receipts  backwards,  we  have  to  figure  at  5  per  cent. 
— 2)4  per  cent.  =  2}i  per  cent. 

3.  The  present  value  of  all  annual  receipts  is  $25,000 

0.050 — 0.035 

4.  The  present  value  of  all  expenses  (taxes  and  protection)  it 
100,000  X  0.05 

005 

EQUATION  :  25,000         100,000  x  0.05  _ 

0.050—0.025  0.05  ~  ^ 

RESULT  :    $900,000  for  the  whole  forest,  or  $9  per  acre. 


ANOTHER  LONGLEAF  PINE  PROBLEM  (FLA.) 

PREMISES  :  Near  Pensacola,  Florida,  a  tract  of  50,000  acres 
stocked  with  longleaf  pine,  not  boxed  for  turpentine,  is  for  sale,  the 
stumpage  averaging  3000  feet  board  measure  per  acre.  The  present 
owner  offers  the  stumpage  alone  at  $1  per  thousand  feet,  or  else  is 
willing  to  sell  the  fee  simple  (soil  and  trees  together)  at  $3.50  per 
acre. 

Under  conservative  lumbering,  the  annual  production  of  timber 
is  133  feet  board  measure  per  acre,  to  be  drawn  from  a  growing 
stock  of  1500  feet  board  measure  per  acre.  The  land  itself  is  prac- 
tically unfit  for  farming.  No  damage  is  to  be  feared  from  forest 
fires,  as  long  as  turpentine  is  not  obtained  from  the  forest.  Figure 
at  6  per  cent,  interest,  and  at  ic  taxes  per  acre  per  annum. 

QUESTION  :  Is  it  advisable  for  a  Pensacola  mill  firm,  of 
twenty-five  million  feet  annual  capacity,  to  buy  the  stumpage  alone, 
or  is  it  more  profitable  for  it  to  acquire  stumpage  and  land  together 
with  a  view  of  practicing  forestry  ? 

POINTS: 

1.  When  buying  the  fee  simple,  the  firm  can  cut,  within  three 
years,  1500  feet  per  acre— the  biggest  trees— leaving  the  balance  of 
1500  feet  on  the  ground,  and  obtaining  from  that  balance  henceforth 
on  an  annual  average  as  much  as  the  annual  accretion,  namely  133 
feet  board  measure  (worth  13.3  cents)  per  acre. 

2.  Thus  the  firm  obtains  from  the  forest 

(a)  For  three  years  annually  500  x  50,000  feet  board  measure 
worth  $25,000. 

(b)  From  the  fourth  year  on,  annually  133  x  50,000  feet  board 
measure  worth  $6,650. 

3.  The  expense  for  taxes  will,  for  the  whole  tract,  amount  to 
$500  annually. 

4.  The  firm  paying  $3.50  x  50,000  equal  to  $175,000  cash 
obtains  assets  worth     25000  (1.06*— i)    ,         6650  500 

0.06  X  1.06^        '   1.06^  X  0.06  0.06 

EQUATION  :     Entrepreneur's  Gain 

25000  (1.06=^-1)  ^       6650  500        ^ -QQQ 

0.06  X  1. 06^        '    1.06^x0.06  0.06 

=  25000  X  2.67  -{-  6650  X  14.0  —  500  X  16.7  —  175000 

=  66750     ]  93100    —  8350   —  175000 

RESULT :  Bent  on  forestry,  the  firm  seemingly  incurs  an 
undertaker's  loss  of  about  $25,000,  paying  more  for  the  forest  than 
the  forest  is  able  to  refund. 

If,  however,  the  prices  of  stumpage  can  be  expected  to  rise  by 
50  per  cent,  in  the  course  of  the  next  20  years  (corresponding  with  a 


rise  of  2  per  cent,  per  annum),  acquisition  of  tiie  fee  simple  at  $3.50 
per  acre  implies  a  net  gain  of  about  $33,600. 

In  addition  it  must  be  remembered  that  the  tract,  under  destruc- 
tive lumbering,  cannot  be  logged  over  in  less  than  six  years,  the  mill 
capacity  being  25  million  feet  board  measure  only. 

Thus  the  firm,  when  engaging  in  ordinary  lumbering,  pays  in 
fact  more  than  $1.00  per  looo  feet  board  measure,  namely 
$150,000  X  0.06  X  1. 06^ 

25,000  (1.066  —  I)      ""  ^^-22 

If  this  consideration  holds  good,  acquisition  of  fee  simple  and 
practice  of  forestry  is  preferable  even  under  stagnating  prices, 
being  by  about  $11,700  superior  to  destructive  lumbering. 


A  RED  FIR  PROBLEM  (OREGON). 

PREMISES  :     Mr.  W r,   a   Michigan    lumberman,  had    a 

chance  to  acquire,  in  1862,  200,000  acres  of  splendid  white  pine  forest, 
at  40c  per  acre.  He  had  made  7  per  cent,  on  the  investment,  and  a 
total  net  gain  of  $1,200,000  when  the  last  tree  was  cut  in  1888. 

In  1900  Mr.  W r  moved  to  Oregon,  and  had  a  chance  in  the 

Cascade  backwoods  to  exactly  repeat  the  speculation  of  1862,  buy- 
ing 200,000  acres  of  splendid  Douglas  fir,  scaling  30,000  feet  board 
measure  per  acre,  at  40c  per  acre. 

The  value  of  the  denuded  land,  in  Michigan  and  Oregon,  is  nill. 
Taxes  ic  per  acre  per  annum. 

QUESTION  :    What  must  be  the  development  of  stumpage 

prices  in  the  section  referred  to,  if  Mr.  W r  is  again  to  make  a 

net  gain  of  $1,200,000  in  addition  to  deriving  7  per  cent,  from  the 
investment,  in  the  course  of  26  years  ? 

POINTS : 

The  answer  depends  on  the  rate,  at  which  the  railroad  system 
in  the  section  will  be  developed,  by  the  establishment  of  which  the 
gradual  removal  of  the  timber  will  be  made  possible. 

I.  Suppose  cutting  begins  after  16  years,  in  I9i6and  ends  in 
1926. 

1.  The  average  cut  will  be  600  million  feet  board  measure  per 
annum,  worth  6oo,oooX.  The  receipts  for  stumpage,  in  1926,  will 
have  accumulated  to         600,000  X  (1.07'°  —  i) 

0.07 

2.  The  accrued  expense  for  taxes  will  be,  at  ic  per  acre  per 
annum,  2000  (1.07^^  —  i) 

0.07 
if  we  assume,  that  taxes  on  the  whole  land  are  paid  until  1926. 

3.  The  original  price  paid  for  the  land,  $80,000,  has  grown  up, 
at  7  per  cent,  compound  interest,  to  year  1926,  to  $80,000  x  1.07-'^. 

EQUATION  : 

600,000  X  ( 1 .07'"  —  I )      2000  ( 1 .072**—  I ) 
1,200,000  =  ^^  -  ^^  _  80,000  X  1.0726 

RESULT:  The  stumpage  price  of  Oregon  pine,  in  that  sec- 
tion, must  average  about  22  cents  per  1000  feet  board  measure,  from 
16  years  from  to-day  on. 

II.  Suppose  cutting  begins  after  10  years,  in  1910,  and  ends  in 
1926. 

I.     The  average  cut  will  then  be  6,000,000,000  =375  million  feet 

16 


board  measure  per  annum.      The  receipts  from  stumpage  in   1926 
will  have  accumulated  to  375,000  X  (1.07^^  —  i) 

2.  and  3.  asunder  I.  0.07 

EQUATION : 

..«o,ooo=    ^"■°°°^.'„7'"-"-'gg^i^g^=il-8.,..ox...7» 

RESULT  :  The  stumpage  price  of  Oregon  pine,  in  that  sec- 
tion, must  average  about  17  cents  per  1000  feet  board  measure,  from 
10  years  from  to-day  on. 


II     II 


II     II 


II     II 


II     II 


A  YELLOW  POPLAR  PROBLEM  (N.  C). 

PREMISES  :    A  careful  tally  of  the  yellow  poplar  trees,  stand- 
iug  in  the  valley  drained  by  Claw  Hammer  creek,  furnishes  the  fol- 
lowing data  : 
1090  trees  of  1%  foot  diameter,  containing  300  feet  b.  m.  each, 

equal  to 327,000  feet  b.  m. 

1980  trees  of  2  foot  diameter,  containing  450  feet 

b.  m.  each,  equal  to 891,000 

860  trees  of  2>^  foot  diameter,  containing  700 

feet  b.  m.  each,  equal  to 602,000 

680  trees  of  3  foot  diameter,  containing  1000  feet 

b.  m.  each,  equal  to 680,000 

270   trees  of  over   zVz  foot  diameter,  containing 

1700  feet  b.  m.  each,  equal  to 459,000 

The  stumpage  of  these  trees  is  worth,  on  an  average. 
In  the  case  of  trees  of  i>^  foot  diameter,  .  $0.75  per  1000  feet  b.  m. 
In  the  case  of  trees  of  2  foot  diameter,  .  .  1.25  per  1000  feet  b.  m. 
In  the  case  of  trees  of  2}^  foot  diameter  .  2.50  per  1000  feet  b.  m. 
In  the  case  of  trees  of  3  foot  diameter  .  .  4.25  per  1000  feet  b.  m. 
In  the  case  of  trees  of  over  z}i  foot  diameter    6.25  per  1000  feet  b.  m. 

The  trees,  up  to  2%.  foot  in  diameter,  are  growing  at  a  rate  of 
lyi  inches  in  10  years,  and  thereafter  at  a  rate  of   i  inch  in  10  years. 

The  taxes  are  not  apt  to  be  reduced  after  the  timber  is  cut. 

The  owner  believes,  that  the  price  of  poplar  stumpage  will 
double  in  25  years  (annual  increase  of  2}^  per  cent),  and  is  satisfied 
to  make  5  per  cent  on  the  investment. 

QUESTION  :  At  what  rate  shall  the  owner  dispose  of  the 
trees,  viz.  down  to  what  diameter  limit  is  it  advisable  for  him  to 
sell  the  trees  ? 

POINTS  : 

1.  Atreeof  I  j^  foot  diameter,  in  40  years,  attains  2  footdiameter 
A  tree  of  2  foot  diameter,  in  40  years  attains  .  .  2%  foot  diameter 
A  tree  of  2>^  foot  diameter,  in  60  years  attains.  .  3  foot  diameter 
A  tree  of  3  foot  diameter,  in  60  years  attains  .  .    .    2%  foot  diameter 

2.  The  lyi,  foot  tree,  now  worth  $0.75  x  0.300  =  22>^  cents, 
will  be  worth  after  40  years  $1.25  x  0.450  x  i.o2S«'  =z  .  .  .  $  1.52 
The  2  foot  tree,  now  worth  $1.25  x  0.450  =  56  cents,  will  be 

worth  after  40  years  $2.50  X  0.700  X  1.025^  = 4.72 

The  2>^  foot  tree,  now  worth  $2.50  x  0.700=  175  cents,  will 

be  worth  after  60  years  $4.25  x  i.ooo  x  1.025'*  =  •  •  18.70 
The  3  foot  tree,  now  worth  $4.25  x  i.ooo  =  425  cents,  will  be 

worth  after  60  years  $6.25  x  1.700  x  1.025^  =    .    .    .    .         46.80 

3.  All  trees,  growing  at  a  5  per  cent,  rate,  are  to  remain  ;  those 
growing  at  a  rate  of  less  than  5  per  cent,  will  be  cut. 

10 


EQUATIONS  : 

For  lYi  foot  trees  :    0.225  x  i.oX*"  =    1.52;    X  =  5     per  cent. 

For  2     foot  trees  :    0.562  x  i.oX*^  =    4,72;    X  =  S/4  per  cent. 

For  2y^  foot  trees  :    1.750  x  loX^"  =  18.70;    X  =  4     per  cent. 

For  3     foot  trees:     4.250  x  i.oX«o  =  46.80;    X  =  4     per  cent. 

RESULT :  The  owner  should  dispose  of  all  trees  having  a 
diameter  of  2}4  foot  or  more,  as  they  grow  only  at  a  rate  of  4  per 
cent.  Obviously,  unsound  trees  which  are  apt  to  deteriorate,  should 
be  cut  at  once  whatever  the  diameter  be. 


II 


ANOTHER  YELLOW  POPLAR  PROBLEM  (N.C.) 

PREMISES:  Pisgah  forest  contains  40,000  acres,  stocked 
with  60  million  feet  board  measure  yellow  poplar  of  superior  quality, 
worth  now  $3.50  per  thousand  feet  board  measure.  The  owner 
expects  that  the  prices  of  yellow  poplar  stumpage  will  double  within 
the  next  15 years  (increase  of  5  per  cent,  per  annum),  and  that  then 
small  logs  and  defective  logs  will  have  a  value  as  well,  so  that  70 
million  feet  board  measure  will  be  available  in  the  year  1915. 

The  taxes  and  the  general  expenses  take  six  cents  per  acre  per 
annum 

The  value  of  the  soil,  after  the  timber  is  cut,  can  be  assumed  to 
be  $2  per  acre. 

The  owner  figures  at  6  per  cent,  interest. 

QUESTION  :  What  is  the  profit  from  the  investment,  if  any 
at  the  end  of  the  next  15  years,  aside  from  the  interest  of  6  per  cent? 

POINTS: 

1.  The  present  value  of  the  investment  is  $60,000x3.50  for  the 
trees  and  $40,000  x  2.00  for  the  soil. 

2.  The  value  of  the  forest  in  1915  is  $70,600  x  7.00  for  the  trees 
and  $40,000  X  2.00  for  the  soil. 

3.  The  running  expenses  from  1900  to  1915  are,  per  annum, 
$0.06  X  40,000.        They  accumulate  up  to  1915,  to  the  sum 

0.06  X  40,000  (1.06'^  —  I ) 

0.06 

EQUATION  :      X  =  70,000  x  7.00  J^  40,000  x  2.00   — 

0.06  X  40,000  (i.o6'5  _  i) 
1.061^(60,000  X  3.50  -\-  40,000  X  2.00) ^-^ 

RESULT  :  The  owner  will  find  himself  $182,000  short.  He 
will  lack  a  good  deal  from  making  6  per  cent,  on  his  investment. 
As  a  matter  of  fact,  he  will  make  about  4  per  cent,  on  the  invest- 
ment and  no  more,  unless  the  stumpage  prices  do  more  than  double 
within  the  next  15  years. 


13 


AN  ADIRONDACK  PROBLEM. 

PREMISES  :  A  tract  of  land  in  the  Adirondacks,  acquired  in 
the  year  1876  at  $5  per  acre,  was  cut  over  in  i888,  yielding  then, 
per  acre,  1800  feet  b.  m.  White  pine,  worth  $3  per  thousand  feet 
b.  m.,  and  2600  feet  b.  m.  Spruce,  worth  $1  per  thousand  feet. 

In  the  year  1896,  there  were  cut  per  acre  another  6550  feet  b.  m. 
of  spruce,  worth  $1.50  per  thousand  feet  b.  m. 

The  taxes  on  the  forest  were  Sc  per  acre  per  annum ;  the 
expense  of  administration  and  protection  2c  per  acre  per  annum. 
Figure  at  6  per  cent. 

QUESTION  :  At  what  cost  were  those  last  6550  feet  b.  m. 
produced  ? 

POINTS: 

I.  The  price  paid  for  the  land,  in  1876,  was  $5  per  acre,  which 
accrued,  at  compound  interest,  and  up  to  the  year  1896,  to  $5.00x1.06^ 

a.  The  running  expenses,  during  the  period  1876  to  1896,  were 
7  cents  per  acre  per  annum,  and  sum  up  to  the  amount  of 

0.07  (1.06^0  —  I) 
0.06 

3.  The  yield  made  in  1888  was  $3.00  x  1.8  J-  $1.00  x  2.6=$8.oo 

Discounted   forward   to   the   year   of  calculation,    1896,  this   yield, 

(which   is  of  course  to   be  subtracted   from  the  various  outlays) 

amounts  to  $8.00  x  1.06^. 

EQUATION:    ^  ^,„      0.07(1.0620-1) 

X  =  5  x  I.O620  -f  ~^-\;^ -  8x  i.o6« 

RESULT  :  The  cost  of  producing  those  6550  feet  was  $5.80. 
As  the  value  of  the  6550  feet  is  $9.82,  the  owner  has  gained,  aside 
from  making  6  per  cent,  interest  on  the  investment  and  aside  from 
having  the  value  of  the  culled  forest  for  an  additional  asset,  about 
$4.00  per  acre. 


13 


A  SPRUCE  PROBLEM. 

PREMISES :  A  spruce  forest  contains  in  the  year  1899  per 
acre  about  4228  feet  b.  m.,  consisting  of  trees  scaling  10  inches  or 
more  at  four  feet  from  ground. 

First  case  :  Suppose  that  the  owner  actually  cuts  down  to  10 
inches  diameter,  thus  removing  now  4228  feet.  Then,  in  the  year 
1929  he  will  be  able  to  again  cut  2420  feet  b.  m.,  cutting  again 
down  to  10  inches.  Every  34  years  thereafter  he  will  have  the 
same  yield  of  2420  feet  b.  m.  The  price  of  the  stumpage  is  $1.40 
per  thousand  feet.  The  taxes  are,  on  an  average,  3c  per  acre  per 
annum. 

Second  case  :  Suppose  the  owner  cuts  only  down  to  12  inches. 
Then  the  forest  will  yield,to  begin  with,36o8  feet  b.  m.  In  the  year  1919 
the  owner  will  be  able  to  cut  2115  feet  b.  m.,  and  thereafter  the  same 
amount  every  24  years.  The  value  of  stumpage  in  this  case  is  $1.50 
per  1000  feet.  The  taxes  are,  on  an  average,  4c  per  acre  per 
annum. 

Third  case  :  Suppose  the  owner  cuts  only  down  to  14  inches. 
Then  the  first  yield  will  be,  in  the  year  1899,  2846  feet  b.  m.  In  the 
year  1919  the  owner  will  be  able  to  cut  2624  feet  b.  m.,  and  thereaf- 
ter every  21  years  the  same  amount.  The  value  of  the  stumpage  is 
$1.60  per  thousand  feet;  the  taxes  are,  on  an  average,  5c  per  acre 
per  annum. 

The  owner  wants  to  derive  5  per  cent,  interest  and  believes  in  a 
gradual  increase  of  the  prices,  the  increase  to  average  2  per  cent, 
per  annum.  The  cost  of  administration  and  protection  is  in  all  cases 
5c  per  acre. 

QUESTION  :  Had  the  owner  of  the  forest  better  cut  down  to 
10  inches,  to  12  inches  or  to  14  inches? 

POINTS: 

1.  The  maximum  difference  between  expected  yields  and  ex- 
pected expenses  determines  the  best  course  to  be  followed. 

2.  In  the  10  inch  case  the  yields  are 

1.03*  X  2,420  X  1.40  «-  ,^ 

4,228x1.40     -L   1.03^^  -  I ^    *      * 

In  the  12  inch  case  the  yields  are 

,    „  ,  1.03*      X    2,115  ^  I-SO  (to  o 

3,608x1.50    ^-  1.0324     -     I  =    ^^'^^ 

In  the  14  inch  case  the  yields  are 

2,846x1.60    4-      1.03x2,624x1.60        _    ^^^^ 

3.   In  the  10  inch  case  the  expenses  are  0.03    -\-    0.05    $1  60 

0.05  ~ 

*4 


In  the  12  inch  case  the  expenses  are  0.04    -\-    0.05  ,.    q 

0.05 
In  the  14  inch  case  the  expenses  are  0.05    -p    0.05  « 

0.05 
EQUATION  :  (8.14  -  1.60)  =  (8.86  -  1.80)  =  (9.56  -  2.00) 

6.54  7-o6  7.56 

RESULT :  Cutting  down  to  14  inches  only,  the  most  con- 
servative practice,  pays  best.  It  pays  by  $1  per  acre,  better  than  cut- 
ting down  to  10  inches,  and  by  Soc.  per  acre,  better  than  cutting 
down  to  12  inches. 


IS 


ANOTHER  SPRUCE  PROBLEM. 

PREMISES:  A  lumberman  owns  20,000  acres  of  spruce  land, 
from  which  he  has  just  cut  6000  feet  board  measure  per  acre,  Z2 
inch  and  over  in  diameter  at  the  stump,  worth  $1.50  per  thousand. 
After  another  20  years  he  will  be  able  to  obtain  3320  feet  per  acre, 
cutting  again  down  to  12  inch  diameter,  and  we  may  expect,  that, 
after  40  years,  the  same  yield  will  be  obtainable  and  so  on. 

The  land,  when  cleared,  is  said  to  have  some  value  for  pasture 
purposes.  The  taxes  are  4cts.,  the  expense  for  administration,  pro- 
tection, etc.,  8  cts.  per  acre  per  annum.     Figure  at  6  per  cent. 

QUESTION  :  What  is  the  forest  worth  at  the  present  mo- 
ment? 

POINTS: 

1.  After  20,  40,  60  (and  so  on)  years,  a  yield  of  3320  feet  b.  m., 
worth  $4.98  can  be  obtained. 

2.  The  necessary  expenses  are  4  cents  plus  8  cents  per  acre 
per  annum. 

3.  The  value  of  a  forest,  like  the  value  of  a  house  or  a  farm  or 
a  business  is  equal  to  the  present  value  of  all  returns,  minus  all  ex- 
penses, expected  from  it. 

EQUATION:    X=      ,^T  "^    =  "•""    "    "^^ 

RESULT  :  The  forest,  after  lumbering,  is  worth  22cts  per  acre. 

If  the  owner  can  sell  it,  for  farming  purposes,  at  over  22cts.  per 
acre,  he  should  certainly  do  it,  provided  that  he  can  make,  by  re- 
investing the  proceeds  of  the  sale,  6  per  cent,  in  an  equally  safe 
manner. 

If  the  taxes,  or  the  expense  necessary  for  administration,  pro- 
tection, etc.,  are  2cts  higher  per  acre  per  annum  than  is  supposed  in 
the  premises,  the  owner  had  better  give  up  the  land  after  the  first 
cutting,  unless  he  can  sell  it,  for  in  that  case  its  forestry  value  is 
negative,  the  necessary  expenses  devouring  all  possible  profits. 

If,  on  the  other  hand,  there  is  a  good  chance  for  the   stumpage 

prices  to  rise,  say  at  the  average  rate  of  2  per  cent,  per  annum,  the 

cut  over  forest  has  a  value  of 

4.08  0.12  _ 

-^-^ 7-    =    $2.15  per  acre. 

1. 042*— I       0.06 

The  study  of  future  prices  of  stumpage  is  of  the  very  greatest 

importance  for  the  wood-owner. 


z6 


A  WHITE  PINE   PROBLEM  (MINNESOTA.) 

PREMISES  :  A  Minnesota  lumberman  owns  10,000  acres  of 
white  pine  forest,  containing  6000  feet  b.  m.  per  acre,  worth  $3  per 
thousand.  The  agricultural  value  of  the  land  is  $5  per  acre,  when 
the  timber  is  removed.  Under  conservative  lumbering,  an  annual 
production  of  300  feetb.  m.  per  acre  can  be  expected.  Taxes  Sets  per 
acre  per  annum.  Protection  from  fire,  under  forestry, i2cts  per  acre  per 
annum.  Extra  logging  expenses,  under  forestry,  $4  per  acre,  at 
the  first  cutting.  Lumber  prices  expected  to  double  in  35  years 
(=  annual  rise  of  2  per  cent.)  Proper  growing  stock  for  forestry 
2000  feet  b.  m.  per  acre. 

QUESTION  :  What  interest  on  the  investment  will  forestry 
yield  ? 

POINTS: 

1.  The  investment,  to  begin  with,  is  6000  feet  b.  m.  worth 
$3  —  $18  per  acre  plus  value  of  soil  worth  $5  per  acre. 

2.  The  yield  under  forestry  is  4000  feet  worth  $3  =  $12  per 
acre  to  be  derived  at  once,  and  300  feet  worth  poets  to  be  derived 
annually  thereafter,  being  the  annual  production  of  the  2000  feet  left 
standing,  per  acre.  The  future  yields  are  to  be  discounted  at  (X 
per  cent.  —  2  per  cent.) 

3.  The  annual  expenses,  under  forestry,  are  20  cents.  The 
extraordinary  expenses  are  $4  per  acre,  spent  at  the  first  cutting. 

EQUATION  :  18  i  5  =  12  ^ # _     '^°     _  4 

^  ^  ^  '  0.0  X  —  0.02         o.oX        ^ 

RESULT:     About  7  per  cent. 


17 


A  SHORT  LEAF  PINE  PROBLEM  (ARK.) 

PREMISES:  The  S.  &  A.  Lumber  Co.,  of  B.,  Arkansas, 
owns  100,000  acres  of  forest  stocked,  per  acre,  with  6000  feet  board 
measure  merchantable  short  leaf  pine,  and  has  a  mill  of  thirty 
million  feet  board  measure  annual  capacity.  The  stumpage  is  worth 
$1  per  1000  feet  board  measure.  The  land  is  unfit  for  agriculture. 
Under  conservative  cutting  the  forest  will  continuously  produce  200 
feet  board  measure  per  acre  per  annum,  after  the  "Virgin  Surplus" 
of  the  forest,  consisting  per  acre  of  4500  feet  of  hypermature  and 
mature  trees,  has  been  removed.  Under  conservative  cutting,  the 
logging  expenses  are  10  cents  higher  per  thousand  feet  board  meas- 
ure. Prices  are  expected  to  rise  at  i  1-2  per  cent  per  annum.  Fig- 
ure at  6  per  cent.  Taxes  are  ict  per  acre  per  annum.  Protection 
from  fire,  under  conservative  lumbering,  will  cost  3cts  per  acre  per 
annum. 

QUESTION:  Which  pays  better,  conservative  or  exhaustive 
lumbering  ? 

POINTS: 

1.  If  prices  rise  at  i  1-2  per  cent.,  future  yields  must  be  dis- 
counted back  to  the  present  moment  at  6  per  cent  —  i  1-2  per 
cent  equal  to  4  1-2  per  cent. 

2.  Under  exhaustive  lumbering,  the  forest  will  yield  30,000,000 
feet  b.  m.  for  20  years,  and  nothing  more.  The  land,  being  non- 
agricultural,  will  be  thrown  away  after  20  years.  The  value  of  all 
yields  expected  from  the  forest,  minus  taxes  for  20  years,  is  there- 
fore : 

30000        (1.0452"    —    i)       1000  (i.o62o    —    i) 

0.045  X  1.045^  0.06  X  1.0620 

3.  Under  conservative  lumbering,  we  withdraw  as  well  annu- 
ally 30  million  feet  from  the  forest,  as  long  as  the  mature  stock  of 
4500  X  100,000  equal  to  450  million  feet  lasts,  namely  for  15  years. 

4.  From  the  i6th  year  on,  we  cut  only  the  annual  production, 
namely,  200  x  100,000  equal  to  20  million  feet  per  annum. 

5.  As  the  extra  logging  expenses,  in  this  case,  are  10  cents 
higher,  the  timber  has  a  stumpage  value  of  90  cents  only,  instead  of 
$1  per  1000  feet  board  measure. 

6.  Taxes  and  protection  from  fire  will  cost  annually  0.04  x 
100,000  equal  to  $4000. 

7.  Thus,  under  conservative  management,  the  present  value 
of  all  expected  yields,  minus  expenses  for  taxes  and  protection  is  : 

27000  (1.045^^ — i)        I    18000 4000 

0.045x1.04515  ~  0.045x1.045^5        ~  ^;5J5 


18 


EQUATION  : 
30000    (1.045^  —  I)  1000  (1.06^)   >^       27000  (1.045^^  —  I)    , 

0.045x1.04520  o.o6xi.o6»>       <  0.045x1.045'* 

18000  4000 

0.045x1.045'^         ~  0.06 

30000x13.0    —    loooxii.s    =   27000x10.7  -}-  400,000x0.5    —    66,700 
RESULT:    Conservative  lumbering  pays,  by  about  $43,700, 
better  than  exhaustive  lumbering. 


«9 


INFLUENCE  OF  FOREST  FIRES  ON  RATE  OF 

INTEREST. 

PREMISES:  Absolutely  safe  investments  (f.  i.  U.  S.  bonds) 
yield  about  3  per  cent,  interest  on  the  principal. 

Forestry  in  America  is  a  less  safe  investment.  Of  course,  trees 
live  and  grov7  as  sure  as  the  sun  shines,  the  wind  blows  and  the 
rain  falls,  for  sunshine,  air  and  rainwater  are  the  components  of 
wood  fibre.  Still  the  ravages  of  forest  fires  endanger  both  capital 
and  returns  from  capital. 

In  the  Southern  Alleghanies,  2  per  cent,  of  the  woodlands,  on 
an  average,  are  annually  damaged  by  fire.  Nature  will  require  20 
years  for  the  restoration  of  the  burned  forest  to  its  former  value  and 
productiveness. 

QUESTION  :  What  is  the  minimum  rate  of  annual  interest 
which  forest-growth,  under  these  conditions,  must  yield  ? 

POINTS: 

1.  98  acres  out  of  100  acres  are  left  intact,  2  acres  out  of  100 
acres  suffer  a  reverse  resulting  in  a  setback  of  20  years. 

2.  Hence  the  value  of  those  2  acres  is  reducd  to  yao  of 
what  it  was  to  begin  with. 

3.  The  growth  of  every  98  units  of  value  left  intact  must 
make  up  for  the  loss  through  burning  in  such  a  way,  as  to  bring  the 
value  of  the  total  investment,  at  the  end  of  the  year,  up  to  103. 

4.  The  98  develop  into  the  value  98  x  i.oX.  This  value,  plus 
what  remains  of  the  2  units  damaged  by  fire,  must  be  103  if  the  in- 
vestor shall  make  3  per  cent,  on  the  original  principal. 

EQUATION  :    98  x  i.oX    '    — %^  =-  103 

RESULT  :  4  1-4  per  cent.  Unless  those  sections  of  the  forest, 
which  are  left  intact,  grow  at  a  rate  of  4  1-4  per  cent.,  the  owner 
does  not  make  3  per  cent,  of  absolute  interest  on  the  whole 
investment.  It  will  pay  the  owner  to  annually  spend  up  to  i  1-4 
per  cent,  of  the  investment  for  forest  protection,  if  by  such  expen- 
sive precaution  fires  can  be  entirely  avoided. 

Where  fires  result,  on  the  annual  average,  in  the  entire  destruc- 
tion of  5  per  cent,  of  the  forest,  the  annual  production  on  areas  left 
intact  must  amount  to  at  least  8.4  per  cent,  if  the  entire  investment 
is  to  bring  3  per  cent,  interest.  Such  a  production  is  impossible, 
unless  the  price  of  standing  timber  doubles  within  the  next  15 
years. 


20 


STUMPAGE  PRICES  OF  THE  FUTURE. 

PREMISES:  Virgin  forest  is  unproductive,  because,  annu- 
ally, just  as  much  timber  is  lost,  through  death  and  decomposition 
of  trees,  as  there  is  produced  under  the  influence  of  sun,  rain  and 
wind. 

Cut  over  forest  is,  as  a  general  rule,  almost  unproductive, 
owing  to  fires  following  the  removal  of  the  virgin  growth. 

Hence  it  is  safe  to  say,  that  the  annual  production  of  timber  in 
the  700  million  acres  of  American  woodlands  is  not  over  one-fifth  of 
what  it  might  be,  (namely,  200  feet  board  measure  per  acre)  and  is 
not  likely  to  exceed  40  feet  board  measure  per  annum  per  acre,  or 
28  billion  feet  board  measure  on  the  whole. 

The  total  growing  stock  of  timber  in  the  United  States  is  esti- 
mated to  be  900  billion,  and  the  annual  consumption  is  estimated  to 
be  39  billion  feet  board  measure,  (exclusive  of  firewood). 

It  is  expected  that,  after  the  exhaustion  of  the  American  virgin 
surplus  of  timber,  prices  of  stumpage  will  be  at  a  level  with  those 
prevailing  in  No-Surplus  countries,  where,  f.  i.,  prime  white  oak 
stumpage  is  worth  $75  instead  of  $3  here,  and  prime  pine  stumpage 
is  worth  $15  instead  of  $1.50  here,  per  thousand  feet  board  meas- 
ure. 

QUESTION  :  At  what  annual  rate  can  we  expect  the  stump- 
age prices  of  oak  and  pine  to  rise,  whilst  our  surplus  is  being  grad- 
ually exhausted  ? 

POINTS : 

1.  The  annual  consumption  of  timber  exceeds  the  annual  pro- 
duction by  at  least  11  billion  feet. 

2.  Hence  our  surplus  stock  of  900  billion  will  be  consumed  in 

equal  to  82  years. 

3.  After  82  years,  stumpage  of  oak  will  be  worth  about  25 
times,  and  stumpage  of  pine  will  be  worth  about  10  times  of  what 
it  is  worth  now. 

EQUATION  :    Oak  :    3.00  x  i.o  X^^  =  75.00 
Pine  :     1.50  x  i.o  X^^  =  15.00 

RESULT  :  The  price  of  oak  stumpage  can  be  expected  to 
rise  at  a  rate  of  about  4  per  cent,  per  annum ;  the  price  of  pine 
stumpage  at  a  rate  of  about  3  per  cent,  per  annum. 


21 


FOREST  TAXATION  IN  THE  UNITED  STATES. 

PREMISES:  In  America  taxes  depend  on  the  value  of  prop- 
erty. In  the  less  densely  settled  sections,  where  most  of  our  for- 
ests are  situated,  the  taxes  amount  to  i  per  cent,  of  the  property 
value. 

Given  a  forest,  vrhich  when  90  years  old  contains  $20  worth  of 
timber  per  acre.  The  soil  alone,  when  cleared,  is  worth  only  $1 
per  acre.     Rate  of  interest  4  per  cent. 

QUESTION  :  What  taxes  ought  to  be  justly  imposed  upon 
the  owner,— if  taking  i  per  cent,  of  the  forest  value  is  just  taxation 
— at  the  6oth  and  30th  year  of  the  development  of  the  forest,  and 
further,  in  the  year,  in  which  the  seedlings  were  just  starting  ? 

POINTS: 

1.  The  taxes  being  i  per  cent,  of  the  value  of  the  forest,  that 
value — a  prospective  value— must  be  ascertained  for  the  years  60, 
30  and  o. 

2.  The  forest  90  years  old  is  worth  $21.00— $0.21,  the  21  cents 
being  the  amount  of  taxes  due  in  the  year  90, 

go 
$21.00 — $0.21  equals  $^^  x  21 

...      ,  ,  $  99  X  21        $  99  X  21     ^    I 

The  forest  89  years  old  is  thus  worth- ^^  ^  ^  ^^—  ^^^  ^  ^  ^^  x  -_ 


^q"^^  *°       [^] 


21 


100  J     1.04 

The  forest  88  years  old  is  thus  worth       f  99  T  ^    21 

I  100  J    1.042 

The  forest  87  years  old  is  thus  worth       f  99  ]  ^   21 

I  100  J 

3.  The  forest  60  years  old  is  thus  worth 

4.  ""The  forest  30  years  old  is  thus  worth    f 

5.  The  forest  o  years  old  is  thus  worth 

EQUATIONS: 
Taxes  in  forest  60  years  old    i      (     99   1  ^'  ^i 


L  100  J 


100    i^  100  J      1.04^" 


Taxes  in  forest  30  years  old    i     f    99  1  "      21 

L  100  J 


100   L  100  J     1.04^ 
Taxes  in  forest  o  years  old     i      f     99  1  *'     21 

100   I  100  i      1.04** 
RESULT:     At  60  years  4  7-10  cent. 
At  30  years  i  i-io  cent. 
At    o  years     2-10  cent. 

22 


INFLUENCE  OF  TAXES  ON  BUSINESS 
FORESTRY. 

PREMISES  :     The  premises  are  just  as  in  foregoing  problem. 

QUESTION :  To  what  figure  do  the  taxes  (paid  from  the  first 
to  the  90th  year  of  the  forest)  accumulate  up  to  the  time  at  which 
the  timber  is  mature,  namely,  up  to  the  90th  year  ? 

POINTS: 

I.     Taxes  in  the  year  0  of  the  forest  are 

I    r   99  1  ®^    21 


100 


100 


1.04' 


90 


which,  discounted  to 


the  year  90,  amount  to 
2 

to 


21 


L   100   J 


91 


100       I-     100 

Similarly,  the  taxes  paid  in  the  year  i  of  the  forest  accrue 
21 
100    ^-  100 


f     99    ^  90 

I  ]      and  the  taxes  paid  in  the  year 

f     99  1  s** 

— ^^-       and  so  on. 
L   100  J 


2  of  the  forest  accrue  to  — 

100    >-   100 

3.     Thus  the  discounted  values  of  the  taxes  form  a  geometrical 

99 
progression  of  91  numbers,  with  ^^  for  the  constant  factor. 

EQUATION  :     Sum  of  taxes  equal  to 
21  L 100 


100 


LiooJ 


z=2I 


1 100  J 


RESULT:  The  sum  of  taxes  paid,  accrued  at  compound 
interest  is  $12.60,  and  thus  takes  away  60  per  cent,  of  the  final 
yield  obtainable. 

It  is  especially  noteworthy,  that  the  rate  of  interest  used  does 
not  influence  the  accrued  sum  of  taxes  in  the  least.  The  sum  simply 
depends  upon  the  number  of  years  required  to  develop  merchantable 
timber  out  of  seedling  trees. 

It  is  safe  to  say  that,  under  the  conditions  now  prevailing  in 
America,  the  taxes  consume  over  one-half  of  the  value  of  the  yield 
derivable  from  forestry,  if  they  are  "justly  "  imposed.  No  wonder, 
then,  that  people  are  averse  of  engaging  in  forestry. 

If  the  rotation  is  150  years,  the  taxes  curtail  the  final  yield  by 
77  per  cent! 


23 


A  NATIONAL  PARK  PROBLEM  (MINNESOTA). 

PREMISES  :  It  is  proposed  to  establish  a  national  park  in 
Northern  Minnesota,  on  land  unfit  for  farming,  stocked  with  about 
6000  feet  board  measure  pine  timber  per  acre,  worth  $2.50  per 
thousand  feet  board  measure. 

Four  thousand  feet  board  measure,  per  acre  on  an  average,  con- 
sists of  mature  or  hypermature  timber,  whilst  the  balance  is  thrifty, 
and  can  be  expected  to  yield  by  its  own  growth  and  by  giving  rise 
to  a  second  growth,  150  feet  board  measure  per  acre  per  annum, 
under  conservative  management. 

In  this  case  the  first  logging  expenses  •will  by  50  cents  per  acre 
exceed  the  logging  expenses  under  destructive  lumbering. 

Taxes,  protection  from  fire  and  administration  will  take  locts  per 
acre  per  annum.  Five  and  one-half  per  cent,  interest. — Stumpage 
prices  expected  to  double  in  35 years  (corresponding  with  an  annual 
increase  of  2  per  cent.) 

QUESTION:  Will  conservative  lumbering,  in  this  case,  pay 
better  than  destructive  lumbering  ? 

POINTS: 

1.  Under  destructive  lumbering,  the  value  of  the  forests  is  6000 
X  2.50  equal  to  $15  per  acre. 

2.  Under  conservative  lumbering,  4000  feet  are  cut  at  once, 
and  2000  feet  are  left  standing  as  a  permanent  investment,  yielding 
annually  0.150  x  2.50  equal  to  37 )4  cents  per  acre,  from  which  fig- 
ure, however,  the  annual  expenses  of  locts  must  be  deducted. 

EQUATION :     15  ^  10.00  -  0.50  4      °-^75 
<  0.035. 

RESULT :  Under  conservative  lumbering,  an  enterpren- 
eur's  gain  of  about  $2.50  per  acre  is  obtained.  Hence  conservative 
lumbering  pays  better. 

Unless  the  first  logging  expenses  under  forestry  are  by  $3.00  per 
acre  higher  than  is  usually  the  case,  destructive  lumbering  is  finan- 
cially inferior  to  conservative  lumbering. 

After  destructive  lumbering,  the  land  is  left  worthless.  Under 
conservative  lumbering  $10  are  withdrawn  from  the  forest,  and 
there  remains  a  permanent  asset  of  about  $8  per  acre  on  the 
ground,  yielding  SH  Pcr  cent,  interest  per  annum. 


24 


STATE  LOANS  FOR  FORESTRY  PURPOSES. 

PREMISES :  The  state  of  P.  decides  to  engage  in  state  for- 
estry, and  to  that  end  takes  up  a  loan  of  $1,450,000,  at  4  per  cent., 
which  is  to  be  used  as  follows : 

$1,000,000  for  purchase  of  1,000,000  acres  at  the  headwaters  of 
the  rivers, 

$      50,000  for  lawyer's  fees,  surveys,  demarkation,  etc., 

$    150,000  for  roads,  etc., 

$  250,000  for  defraying  the  annual  salaries  of  superintendents 
and  rangers.  After  the  road  system  is  developed,  12  years  from 
today,  an  annual  revenue  of  10  cents  per  acre  per  annum  will  be 
derived,  under  conservative  management,  and  it  is  expected  that 
this  revenue  will  gradually  increase  at  the  rate  of  3  per  cent,  per 
annum. 

QUESTION:  A:  Within  how  many  years  will  the  forest 
itself  be  able  to  redeem  the  loan  ? 

B  :   What  is  the  forest  worth  after  the  loan  is 
redeemed  ? 

POINTS : 

1.  The  annual  interest  on  the  loan  is  $58,000. 

2.  The  revenue  from  the  12th  year  on  is  o.io  x  1,000,000  = 
$100,000,  of  which  $58,000  are  used,  from  that  time  on,  to  pay  the 
interest  on  the  loan,  whilst  $42,000  or  more  are  available  annually 
for  redemption  of  loan. 

3.  As  the  revenue  rises  at  3  per  cent,  per  annum,  the  receipts 

are  to  be  discounted  at  4  per  cent.  —  3  per  cent.  —  i  per  cent. 

EQUATION:       .      42000(1.01"   —    i) 

A:   ^- ^ ^—  1,450,000 

o.oi  X  1. 01"  '^^  ' 

3.      100,000  X  1.03^"    _ 

o.oi  ~ 

RESULT  :    A  :     The  loan  can  be  entirely  redeemed  within  43 

years  after  the  12th  year,  or  within  55  years  from  today. 

B  :     The  forest,  freed    from  all  incumbrances  after 

55   years,  and    producing   annually    $356,000   with   prospect  of  an 

annual    increase    of  revenue    equalling  3  per  cent.,  is  worth  about 

$35,600,000. 

If  the  people  are  ready  to  spend  $58,000  for  12  years,  they  will 

gradually  build  up  a  very  valuable  forest. 

Far-leading  calculations  in  forestry  might  seem  fallacious  and 

absurd,  if  forest-history  had  not  proved  the  very  contrary. 


25 


WEEDING  AND  ROAD-BUILDING. 

PREMISES  :  Given  a  spruce  forest  in  the  Adirondacks, 
containing  50,000  acres  stocked  with  4,000  feet  b.  m.  per  acre.  The 
forest  is  to  be  cut  over  at  once  in  such  a  v^ay  as  to  reduce  the 
average  stumpage  to  1,200  feet  b.  m.,  which  are  expected  to  produce 
thereafter  140  feet  b.  m.  per  acre  per  annum.  Stumpage  is  worth 
$1.50  per  1,000  feet  b.  m.     Cuttings  recur  every  10  years. 

QUESTION :  A  :  Is  it  advisable  for  the  owner,  to  remove,  by 
way  of  an  additional  "weeding,"  the  misshapen  trees  at  an  expense 
of  50  cents  per  acre,  if  by  so  doing  the  annual  production  can  be 
raised  from  140  feet  to  175  feet  b.  m.  per  acre  ? 

B  :  Is  it  advisable  for  the  owner  to  build  the 
skidding  roads  more  solidly,  at  an  expense  of  $10,000  so  as  to  make 
them  available  for  future  operations,  and  so  as  to  be  less  depend- 
ent on  the  snow-covering,  if  by  so  doing  the  logging  expenses 
per  1000  feet  b.  m.  can  be  reduced  by  Sets  ? 

POINTS  :      A  :    The  additional  expense  of  50  cents  results 

in  producing,  every  ten  years,  an  additional  350  feet  b.  m.  worth 

52>^  cents. 

B  :    The  additional  expense  of  $10,000,  reduces 

the  cost  of  logging,    and  hence   increases  the   value  of  stumpage, 

by  5cts  per  1000  feet.     The  first  cut,  therefore,  of  50,000  x  2800  = 

140,000,000   feet   b.  m.,  gains    $7,000  ;  the   subsequent  cuttings,  of 

50,000  X  1750  =  87,500,000  feet  b.  m.,  gain  $4,375. 

EQUATION  :  A  :  0.50  ==  ^^^^ 

B :      10,000  =  7,000  -?-  -^^f 

i.oX'"  —  I 

RESULT:  The  "weeding"  as  well  as  the  solid  construction 
of  roads  are  advisable,  the  former  paying  7  per  cent,  and  the  latter 
g)4  per  cent,  interest  on  the  additional  outlay  required.  The  advan- 
tage derived  is  greater  still,  if  stumpage  prices  are  on  the  increase. 


26 


